Motorists would be pumping a couple dollars into the classroom each time they fill their tank, if departing Gov. Chris Gregoire’s budget proposal wins support.

She suggests a new wholesale excise tax on motor fuel, to fund the yellow school buses that move hundreds of thousands of public-school students every day.

By fiscal 2017, the fuel taxes would cover the full $906 million biennial cost for student transportation — in theory, freeing up $906 million to use in the classroom.

Drivers would pay an added 5 cents a gallon July 1, rising to 8 cents in mid-2015 and 12 cents in mid-2017, if the oil industry were to pass the tax entirely to consumers, according to the Department of Revenue.

Such a tax could make it harder for the Legislature to rescue the ferry system and underfunded road projects, such as widening I-90 east of Snoqualmie Pass, the redecking of half-century-old I-5. The Legislature also would have a harder time relieving an expected $200 million shortfall in toll revenue for the Highway 99 tunnel.

When asked about that dilemma Tuesday, Gregoire replied she steered clear of the funding tools lawmakers already were considering for transportation, such as retail gas tax or car-tab tax. She also argued that oil companies made $60 billion profit in the first half of 2012, so they can absorb the wholesale tax. “You can be skeptical about it, and I can, too, but there is no reason to pass it on — none,” she said.

But Gregoire also acknowledged, “They can do anything they want.”

A Department of Revenue fiscal note presumes the tax would show up at the pump.

Tim Hamilton, executive director of Automotive United Trades Organization, said such taxes would show up as line items on the bills that gas-station operators pay for fuel deliveries.

“It would be like proposing a 15 percent sales tax and claiming Walmart would pay it,” he said.

The Democrats’ choice for Senate majority leader, Ed Murray, D-Seattle, has said he believes voters would likely agree to pay a bit more if the money went to education. “School buses for kids, a little tax on gas — I think the voters would sign off on that,” he said.

The state Joint Task Force on Education Funding voted Monday to include such a move among its recommendations.

But some Democrats have expressed concern that it would hurt other transportation funding.

Judy Clibborn, House Transportation Committee chairwoman, said using a transportation-related tax to fund school buses wouldn’t leave”any room to do transportation for the rest of your state.”

The governor’s proposal calls for a wholesale fuel tax of 1.85 percent next year, 2.91 percent in 2015, and 4.62 percent in 2017.

The state provided $596 million for 2011-13 for K-12 pupil transportation.

That would grow to $869 million for 2013-15, because the state would take on more of the bus costs now paid by local districts — freeing up dollars for many of them.

An existing 50-cent per gallon beer tax and a 0.3 percent business services tax would be extended through 2017, to partly fund buses.

By 2017 the fuel tax would be high enough to fully support a $906 million state school-bus budget.